Relativistic momentum is 1% greater than classical, at what speed?

  • Thread starter chris_0101
  • Start date
  • #1
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Homework Statement


How fast must a body be traveling if its forrect relativistic momentum is 1% greater than the classical momentum


Homework Equations


P_r = mv/sqrt(1-(v^2/c^2))
P_nr = mv
p_r = 1.01P_nr

The Attempt at a Solution



mv/sqrt(1-(v^2/c^2)) = 1.01mv
mv = 1.01(mv)[sqrt(1-(v^2/c^2))]
1 = 1.01[sqrt(1-(v^2/c^2))]
1/1.01 = sqrt(1-(v^2/c^2))
(1/1.01)^2 = 1-(v^2/c^2)
0.980296 = 1-(v^2/c^2)
0.980296 - 1 = -(v^2/c^2)
-0.01970 = -(v^2/c^2)
(-0.01970)(c^2) = -v^2
0.01970c^2 = v^2
0.0003884c = v

However, this is not the correct answer. The actual answer in the back of the textbook is 0.14c. If anyone can correct my algebra or point me into the right direction it would be greatly appreciated.

Thanks
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
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0.01970c^2 = v^2
0.0003884c = v

The square root of 0.01970 is not 0.0003884 :wink:
 
  • #3
65
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I cannot believe I overlooked that, it turned out I was squaring the 0.01970. Thanks a lot :)
 

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